fix(rds): read replica instance cannot join domain (#19202)

The read replica instance always uses the same engine as the source instance
but some CF validations require the engine to be explicitely passed when some
properties are specified.

Pass the `engine` property to the CF resource if `domain` is specified.

Closes #18786


----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/@aws-cdk/aws-rds/lib/instance.ts

@@ -1171,12 +1171,18 @@ export class DatabaseInstanceReadReplica extends DatabaseInstanceNew implements
       throw new Error(`Cannot set 'backupRetention', as engine '${engineDescription(props.sourceDatabaseInstance.engine)}' does not support automatic backups for read replicas`);
     }
 
+    // The read replica instance always uses the same engine as the source instance
+    // but some CF validations require the engine to be explicitely passed when some
+    // properties are specified.
+    const shouldPassEngine = props.domain != null;
+
     const instance = new CfnDBInstance(this, 'Resource', {
       ...this.newCfnProps,
       // this must be ARN, not ID, because of https://github.com/terraform-providers/terraform-provider-aws/issues/528#issuecomment-391169012
       sourceDbInstanceIdentifier: props.sourceDatabaseInstance.instanceArn,
       kmsKeyId: props.storageEncryptionKey?.keyArn,
       storageEncrypted: props.storageEncryptionKey ? true : props.storageEncrypted,
+      engine: shouldPassEngine ? props.sourceDatabaseInstance.engine?.engineType : undefined,
     });
 
     this.instanceType = props.instanceType;

packages/@aws-cdk/aws-rds/test/instance.test.ts

@@ -1617,6 +1617,31 @@ describe('instance', () => {
       },
     });
   });
+
+  test('engine is specified for read replica using domain', () => {
+    // GIVEN
+    const instanceType = ec2.InstanceType.of(ec2.InstanceClass.T3, ec2.InstanceSize.SMALL);
+    const engine = rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_13 });
+    const source = new rds.DatabaseInstance(stack, 'Source', {
+      engine,
+      instanceType,
+      vpc,
+    });
+
+    // WHEN
+    new rds.DatabaseInstanceReadReplica(stack, 'Replica', {
+      sourceDatabaseInstance: source,
+      instanceType,
+      vpc,
+      domain: 'my-domain',
+    });
+
+    // THEN
+    Template.fromStack(stack).hasResourceProperties('AWS::RDS::DBInstance', {
+      SourceDBInstanceIdentifier: Match.anyValue(),
+      Engine: 'postgres',
+    });
+  });
 });
 
 test.each([